what equation would i use if i wanted to find the magnitude for this problem
A box of mass 32.0 kg is subject to an applied force (FA) with an elevation angle of 39.9°, and it accelerates to the right at 6.31 m/s2. The horizontal surface has a coefficient of friction μ = 0.147.
To find the magnitude of the applied force (FA) in this problem, you can use the equation involving the forces acting on the box. Here's the step-by-step process:
1. Identify the forces acting on the box. In this case, we have the applied force (FA), friction force (Ffr), and gravitational force (Fg).
2. Break down the forces into their respective components. The applied force (FA) has both horizontal (FxA) and vertical (FAy) components.
3. Since the box is accelerating to the right, the net force in the horizontal direction must be equal to the mass of the box (m) multiplied by its acceleration (a): Fx = max.
4. The horizontal component of the applied force (FxA) is equal to FA * cosθ, where θ is the elevation angle of the applied force.
5. The friction force (Ffr) can be calculated using the formula Ffr = μ * (normal force), where μ is the coefficient of friction and the normal force is equal to the weight of the object (mg).
6. The vertical component of the applied force (FAy) should balance out the vertical component of the gravitational force (Fgy) to keep the box from accelerating vertically: FAy - Fgy = 0.
Combining these equations, we have:
FA * cosθ - μ * (mg) = max (horizontal equation)
FAy - mg = 0 (vertical equation)
You can now rearrange these equations to solve for the magnitude of the applied force (FA).